Polymer 54 (2013) 1639e1646
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Polymer
journal homepage: www.elsevier.com/locate/polymer
Bulk transparent epoxy nanocomposites filled with poly(glycidyl methacrylate)
brush-grafted TiO2 nanoparticles
Peng Tao a, *, Anand Viswanath b, Ying Li a, Richard W. Siegel a, Brian C. Benicewicz b, Linda S. Schadler a, *
a
b
Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States
Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208, United States
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 9 December 2012
Received in revised form
14 January 2013
Accepted 19 January 2013
Available online 25 January 2013
Poly(glycidyl methacrylate) polymer brushes were grafted onto TiO2 nanoparticle surfaces via a combination of phosphate ligand engineering and Cu-catalyzed alkyne-azide “click” reaction. The grafted TiO2
nanoparticles are compatible with a commercial epoxy resin enabling the preparation of thick (1 mm)
transparent high-refractive index TiO2/epoxy nanocomposites. In order to maximize the volumetric
loading and thereby the refractive index of nanocomposites, the minimum graft densities that can lead to
high optical transparency were identified. It was found that, when the graft density was too low to form
polymer brushes, the dispersion of the grafted particles changed from a dispersed state to an agglomerated state. The transition of the dispersion state was in good agreement with the theoretical prediction
from a parametric model. This good agreement will facilitate the design and fabrication of transparent
polymer nanocomposites filled with grafted nanoparticles. With 30 wt% loading of TiO2 nanoparticles,
the refractive index of TiO2/epoxy nanocomposites increased from 1.5 for neat epoxy to 1.62. The
transparency of the prepared nanocomposites can be well predicted by the Raleigh scattering model.
Published by Elsevier Ltd.
Keywords:
Polymer-grafted nanoparticles
Refractive index
Polymer nanocomposites
1. Introduction
Combining the advantages such as high optical transparency
and excellent processability from organic components with the
added functionality from inorganic nanofillers, polymer nanocomposites can exhibit diverse functional properties, and are
already used for a variety of important applications [1e3]. For optical applications such as encapsulation of light emitting diodes
(LEDs), polymer matrices filled with high-refractive-index (high-n)
nanoparticles (NPs) would increase the refractive index of the
encapsulant, and thereby the light extraction efficiency of LEDs [4].
So far, most reported research has been focused on high-n nanocomposite thin films with a typical thickness less than 50 mm [2]. To
be used as high-n LED encapsulant or lens materials, bulk nanocomposites with a thickness of 1 mm are desired. Compared with
various in situ preparation methods, ex situ synthesis of optical NPs
and direct incorporation into the polymer matrix provides the
flexibility of choosing inorganic and organic building blocks with
well-defined properties and thus the possibility of tuning the
properties of the nanocomposites [2]. However, a critical obstacle
to the fabrication of transparent nanocomposites via the ex situ
* Corresponding authors. Tel.: þ1 518 276 2022; fax: þ1 518 276 8554.
E-mail addresses: taop1985@gmail.com (P. Tao), schadl@rpi.edu (L.S. Schadler).
0032-3861/$ e see front matter Published by Elsevier Ltd.
http://dx.doi.org/10.1016/j.polymer.2013.01.032
route is controlling the size and size distribution of functional NPs,
and more importantly the dispersion of inorganic fillers within
polymer matrices since inorganic NPs are prone to aggregation in
polymers [5].
One general and effective approach to dispersing NPs within
a polymer matrix is to graft inorganic NPs with polymer chains
having the same or similar chemical composition as the matrix
polymer [6e9]. Although this particle dispersion approach is successful in the most extensively explored silica/polymer nanocomposite systems, in most cases these NPs were grafted with high
density polymer brushes using surface-initiated “grafting from”
methods [10e13]. By contrast, very few studies have been carried
out in the preparation of transparent thick high-n nanocomposites
via the simple “grafting to” approach. Epoxy represents a class of
thermosetting polymeric materials with extensive and important
industrial applications ranging from coatings to adhesives and
electronic and optical devices packaging such as encapsulation for
LEDs. Therefore, a simple and versatile method to homogeneously
disperse functional NPs in the epoxy matrix is urgently needed.
Grafting inorganic NPs with poly(glycidyl methacrylate) (PGMA)
has been shown to be able to improve the dispersion of NPs within
epoxy matrices and prepare highly transparent thin film coatings
[14,15]. The dispersion of the grafted particles within polymer
matrices has been reported to be affected by the graft density, the
grafted/matrix chain length ratio, as well as the particle size [7e
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P. Tao et al. / Polymer 54 (2013) 1639e1646
9,16e18]. However, very little quantitative information is available
on the dispersion behavior despite the ubiquity of polymers filled
with homogeneously dispersed grafted particles. Thus, a more
quantitative prediction of the dispersion state of grafted NPs would
provide a guideline for practical fabrication of transparent polymer
nanocomposites.
Generally, densely grafted thick polymer layers are desired for
achieving good screening of the NP coreecore attraction and hence
good dispersion in the polymer matrix. On the other hand, to
improve the refractive index of the nanocomposites effectively,
a sufficiently high loading concentration of high-n NPs is needed.
Therefore, achieving good dispersion of high-n NPs within polymer
matrices with the minimum amount of grafted polymer is critical to
the practical fabrication of high-n nanocomposites. In this work, we
experimentally studied the dispersion behavior of PGMA-grafted
TiO2 NPs within an epoxy matrix through varying the graft density and molecular weight of the grafted PGMA chains. We further
built a predictive dispersion phase diagram for the dispersion of
PGMA-grafted TiO2 NPs within the epoxy matrix, which agrees well
with experimental observations. Finally, based upon the comprehensive understanding and effective control of the dispersion
behavior of PGMA-grafted TiO2 particles within the commercial
epoxy matrix, bulk transparent high-n TiO2/epoxy nanocomposites
were successfully prepared.
2. Experimental section
2.1. Materials
Titanium (IV) butoxide (97%, Sigma Aldrich), oleic acid (90%,
Sigma Aldrich), triethylamine (70%, Aldrich) and toluene (99.5%,
Sigma Aldrich) were used for the synthesis of TiO2 nanoparticles.
POCl3 (99.99%) and NaN3 (Sigma Aldrich) and 11 bromo-1undecanol (Acros) were used for synthesis of azido-phosphate.
Cu(I)Br (99.999%, Sigma Aldrich) was purified with acetic acid
and washed with ethanol and diethyl ether three times.
(PMDETA)
was
N,N,N0 ,N00 ,N00 -Pentamethyldiethylenetriamine
obtained from Acros Organics and used as received. Epoxy 301-1
(two parts kit) was purchased from Epoxy Technology. Part A is the
epoxy resin (bisphenol-A diglycidyl ether) with a molecular weight
around 340 g mol1 and part B is the cross-linking agent (triethyl-1,
6 hexanediamine).
transfer (RAFT) polymerization technique, as described in detail
elsewhere [14]. Alkyne-PGMA with other molecular weights was
made with the similar procedure but different reaction durations.
As listed in Table 1, alkyne-PGMA polymers with four different
molecular weights (Mn) and low polydispersity index (PDI, ) were
synthesized with the well-controlled RAFT technique.
A mixture of the as-synthesized anatase TiO2 particles and 11azidoundecyl dihydrogen phosphate with a weight ratio of 1:1
dispersed in chloroform was subjected to stirring at reflux overnight. The phosphate-treated particles were washed with ethanol,
centrifuged and redispersed into chloroform. This precipitationredispersion process was repeated two more times to get the
final azide functionalized particles in chloroform.
In a typical “click” reaction, 0.4 g of phosphate-treated TiO2
particles, 0.5 g of alkyne-PGMA, 20 mL of PMDETA ligand were
added into 60 mL anhydrous THF. 10 mg of CuBr was added into the
flask and the solution was bubbled with argon gas for 5 min. The
flask was then transferred into an oil bath at 55 C for 48 h. The
grafted particles were precipitated with methanol and redispersed
into chloroform. To identify the maximum achievable graft density,
the “click” reaction was carried out with the weight ratio of the
phosphate-treated TiO2 particle to alkyne-PGMA ranging from 1:1
to 1:4. To prepare low graft density PGMA-grafted TiO2 particles,
higher particle to alkyne-PGMA weight ratios (2:1, 4:1 and 6:1)
were used in the “click” reaction.
To remove the possible unattached PGMA, after the “click” reaction, the obtained grafted particle solution was precipitated with
methanol and recovered with high speed (12 000 rpm) centrifugation. The obtained particles were redispersed into chloroform. It was found that the un-grafted PGMA was precipitated on
top of the grafted particles in the centrifuge tube probably due to
the density difference between the pure PGMA polymers and
PGMA-grafted TiO2 particles. During the redispersion process, the
top PGMA layer dissolved first while it took longer time before the
grafted particles were dispersed. The separation of unattached
PGMA was further confirmed by the 100% weight loss from the TGA
measurement of the initially dissolved part. This centrifugation and
redispersion process was repeated for two more times until there is
no change in the TGA weight loss of the grafted particles. At the
same time, the supernatant was checked with an FTIR spectrometer
until there is no any observed alkyne-PGMA peaks.
2.4. Characterization
2.2. Synthesis of TiO2 nanoparticles
The TiO2 nanoparticles were synthesized through a two-phase
synthetic approach where the particles were formed at the interface between the organic and aqueous phase [19]. In a typical
synthesis, to a stainless steel pressure vessel (45 mL, Parr), DI water
(10 mL) and triethylamine (0.5 mL) were added and homogeneously mixed. The organic phase was prepared by mixing the
solution of toluene (20 mL), titanium butoxide (1 mL) and oleic acid
(3 mL) in a separate beaker. Then the organic solution was poured
into the pressure vessel. The vessel was sealed tightly and transferred into an isotemp oven at 200 C for 12 h. After reaction, the
top transparent toluene solution was extracted by a pipette. The
particles were precipitated with ethanol and recovered with
centrifugation.
2.3. Surface modification of TiO2 particles
11-Azidoundecyl dihydrogen phosphate was synthesized with
a simple two-step reaction based on our previous work [15], and
was used as the binding ligand. Alkyne-terminated PGMA was
synthesized with a reversible addition-fragmentation chain
X-ray powder diffraction patterns of the synthesized particles
were obtained with a Bruker D8 Discover XRD diffractometer using
A) and operating at an accelerating
Cu Ka radiation (l ¼ 1.5405 voltage of 40 kV, in the 2q range from 10 to 80 (step of 0.01 ).
Transmission electron micrographs were taken on a JEOL-2010
operating at 200 kV. The TEM samples were prepared by microtoming the composites into 50e70 nm thick slices. The refractive
index dispersion of the composites was measured by variable angle
spectroscopy ellipsometer (VASE, J.A. Woollam Co., Inc. EC-400) on
a spin-coated sample on a Si wafer. The measured results were
fitted with the Cauchy model. Transmittance spectra were obtained
Table 1
Grafted alkyne-PGMA polymers with four different molecular weights synthesized
with RAFT polymerization.
Alkyne-PGMA
Mn (g mol1)
PGMA-5K
PGMA-10K
PGMA-20K
PGMA-56K
4957
12500
20000
58000
1.17
1.22
1.2
1.23
P. Tao et al. / Polymer 54 (2013) 1639e1646
with a PerkineElmer Lambda 950 spectrophotometer using air as
the reference. The nanocomposite samples were prepared by
mixing PGMA-grafted TiO2 particle dispersion in chloroform with
Epoxy 301-1 part A (bisphenol-A diglycidyl ether) and removing
solvent under vacuum. Then, Epoxy 301-1 part B (cross-linking
agent) was added with a weight ratio of 1:4 with respect to part A.
The mixture was poured into a glass mold and heated at 80 C for
30 min. The bulk transparent nanocomposite samples were placed
in perpendicular to the incident light to measure the transmittance.
FTIR spectra were obtained on a Perkin Elmer Spectrum One
FTIR Spectrophotometer scanning from 500 to 4000 cm1 with
a resolution of 4 cm1 for 10 scans. Thermal gravimetric analysis
(TGA) was done on a Perkin Elmer Series 7 instrument. The TGA
samples were thoroughly dried under an oven at 120 C overnight.
The sample was heated from 30 to 700 C under a 60 ml min1
nitrogen flow at a heating rate of 10 C/min. Graft density of PGMA
chains was estimated based on TGA weight loss due to decomposition of the grafted chains with the following equation [20]:
s ¼ ðwNA =Mn Þ= 4pa2 n ¼ arNA 1021 =3ð1 zÞMn
(1)
where w, NA, Mn, a, r, n and z are the weight of organic polymers,
Avogadro’s number, molecular weight of grafted chains, radius of
particles, density of particles, the number of NPs and weight loss of
polymer chains, respectively.
3. Results and discussion
3.1. Grafting PGMA onto TiO2 particles
As shown by Fig. 1, near mono-dispersed, highly crystalline
anatase TiO2 NPs were prepared with a two-phase synthetic
approach. The particle size and size distribution were determined
by sampling 200 particles from the TEM image using Image J
software. It shows a number average size of 5 nm in diameter,
1641
which agrees well with the estimation from the broadening of the
(101) anatase XRD peak using the Scherrer’s formula (5.4 nm). The
as-synthesized TiO2 NPs can be easily dispersed into chloroform
solvent forming a transparent dispersion as demonstrated by the
photograph in Fig. 1c due to the capping of oleic acid during the
synthesis.
As shown in Scheme 1, PGMA chains were grafted onto TiO2 NP
surfaces via a combination of robust organo-phosphate ligand
anchoring and simple Cu(I) catalyzed alkyne-azide “click” reaction
[14,15]. The synthetic oleic acid capping agent on the TiO2 NP surfaces was exchanged with an azido-phosphate ligand which has
a stronger binding capability with TiO2 NPs. The azide terminal
groups allow for the attachment of PGMA chains using “click”
chemistry. The successful attachment of alkyne-PGMA was evidenced by the reduced intensity of the azide group in the FTIR
spectrum as shown by Fig.2. However, after the reaction, a small
residual peak was still observed indicating that not all the surface
azide terminal groups were reacted. This is because the simple
“grafting to” method has a constraint in the maximum graft density
that can be obtained.
To investigate the influence of PGMA molecular weight on the
maximum achievable graft density, alkyne-PGMA with different
molecular weights were grafted onto the same batch of TiO2 NPs.
TGA curves in Fig. 3 show an increased weight loss after grafting
with PGMA chains, further indicating successful attachment via the
simple “click” reaction. Using Eq. (1), the graft densities of PGMA
chains were estimated from the TGA weight loss due to the
decomposition of the grafted PGMA chains. The density and the
radius of the anatase phase particles were estimated to be
3.87 g cm3 and 2.5 nm, respectively. The weight loss of grafted
PGMA chains (z) was calculated by comparing the TGA weight loss
difference between the azido-phosphate functionalized particles
and particles grafted with PGMA chains.
Fig. 4 shows that the graft density (s) scales inversely with the
molecular weight through a power law (swN0:73 ), where N is the
number of repeating units of the grafted PGMA chains. In the
Fig. 1. (a, b) TEM image under low and high magnification; (c) X-ray diffraction pattern and (d) particle size distribution of the synthesized anatase phase TiO2 NPs. The inset shows
a transparent dispersion of the as-synthesized particles within chloroform.
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P. Tao et al. / Polymer 54 (2013) 1639e1646
Scheme 1. Preparation of PGMA-grafted TiO2 NPs via the combination of ligand exchange and “click” chemistry.
“grafting to” method, the amount of polymer that can be attached is
limited for both kinetic and thermodynamic reasons [21,22]. During
the experiment, it was found that the maximum graft density was
determined by the size of the grafted chains and not by the reactant
concentration. The same graft density was obtained when
increasing the reactant weight ratio of alkyne-PGMA to TiO2 NPs
from 1:1 to 4:1. The “click” reaction proceeded very efficiently and
the particle surfaces were quickly coated with a certain number of
PGMA chains. As more and more polymer chains are grafted onto
the surface, the polymer concentration near the particles soon
becomes higher than the concentration in solution. Additional
chains must then diffuse against this concentration gradient to
reach the surface and further attachment of polymer becomes
kinetically hindered. Thermodynamically, as the graft density increases, the grafted polymer chains must adopt a stretched conformation to avoid chain overlap. However, the loss of entropy
during chain stretching is offset only by the formation of a single
chemical bond, so the attachment of further chains rapidly becomes unfavorable. With the maximum achievable graft densities,
the distance between two grafting sites is smaller than twice the
radius of gyration, therefore the PGMA chains grafted to the TiO2
particles exist in a stretched polymer brush regime [22].
3.2. Dispersion behavior of PGMA-grafted TiO2 NPs within epoxy
The grafted PGMA chains have epoxide functional groups
making the grafted TiO2 particle compatible with epoxy resins.
Fig. 5 presents the experimental dispersion phase diagram of the
Fig. 2. FTIR spectra of TiO2 NPs modified by azido-phosphate ligand, alkyne-PGMA10K, and TiO2 NPs click with PGMA-10K.
PGMA-grafted TiO2 particles in the epoxy matrix. With the maximum graft densities, the PGMA-brush-grafted particles showed
a homogeneous dispersion within the epoxy matrix and transparent nanocomposites were obtained. To lower the graft density,
smaller weight ratios of alkyne-PGMA to phosphate-treated particles were used in the “click” reaction. Accordingly, the graft density
decreased continuously and the grafted chains gradually transitioned from brush to mushroom conformation. Near the “brush-tomushroom” transition points, the dispersion of PGMA-grafted TiO2
particles abruptly changed from a homogeneously dispersed state
to an agglomerated state. With lower graft density, the behavior of
the grafted particles more closely resembles unmodified particles
as their surfaces are not fully covered with polymer chains. At very
low graft densities, the strong inter-particle attraction dominates
due to insufficient surface coverage leading to agglomeration.
As shown by TEM images in Fig. 6, the PGMA-10K brush-grafted
TiO2 particles were homogeneously dispersed and individually
separated particles were clearly observed at high magnification.
Similar uniform dispersions of the other molecular weight PGMAbrush-grafted particles are shown by the TEM images in Fig. S1
(see Supplementary Information). At a low graft density, Fig. 6c
and d show that the sparsely grafted particles formed agglomerates
with sizes ranging from sub-micrometer to 50 nm. Near the large
agglomerates, string-like structures of grafted particles were
observed. Under high magnification, the formation of clusters was
clearly seen. This is different from unmodified particles, which
usually form spherical agglomerates within the polymer matrix
due to the isotropic van der Waals attraction between particles. For
the low graft density particles, the grafted PGMA chains need to
Fig. 3. TGA curves of TiO2 NPs modified with an azido-phosphate ligand, and TiO2 NPs
grafted with PGMA chains of different molecular weights.
P. Tao et al. / Polymer 54 (2013) 1639e1646
Fig. 4. Graft density of PGMA as a function of the degree of polymerization N. The inset
shows the plot on a logelog scale with a linear least-square fit.
rearrange their conformation to accommodate the strong coree
core attraction, resulting in the anisotropic string-like morphology in the epoxy resin. As demonstrated in Fig. S2 (see
Supplementary Information), the segregation of low graft density
particles and the formation of connected particle clusters were also
observed for other grafted chain molecular weight. This is the first
time the anisotropic assembly of low graft density particles within
thermosetting polymer matrix was observed similar to that was
reported in the grafted silica polystyrene nanocomposites [8]. The
inhomogeneous dispersion and formation of micro-sized aggregates introduced strong scattering loss of transparency evidenced
by the opaque nanocomposite sample. During the dispersing process, it was noticed that the transition from well-dispersed state to
aggregated state can be easily identified as the graft density
decreased. The obvious transition might be related to the fact that
the low graft density particles encountered an “allophobic dewetting” transition, which is a discontinuous, first-order transition
[18]. The large refractive index mismatch between TiO2 NPs and
epoxy matrix leads to high sensitivity of the transparency of the
nanocomposites to the dispersion state of the NPs.
3.3. Theoretical prediction of dispersion of PGMA-grafted TiO2 NPs
within epoxy
To enable theoretical predictions of the dispersion behavior
of the grafted NPs in the epoxy matrix, we adapted the
Fig. 5. Experimental dispersion diagram of PGMA-grafted TiO2 NPs within an epoxy
matrix. The solid and dash lines represent the maximum achievable graft densities and
the “brush-to-mushroom” transition, respectively.
1643
parametric phase diagram previously reported by Pryamtisyn
et al. [23] for our specific dispersion systems (see
Supplementary Information). As indicated by this model, the
dispersion state of grafted NPs was determined by the balance
between the enthalpic gain from the contact between two NPs
and the entropic repulsion due to the deformation of grafted
chains. The energetic gain was estimated from the van der Waals
attraction between two NPs within the epoxy resin medium.
Given that the synthesized TiO2 particles were capped with oleic
acid, the particles were modeled as coreeshell structured particles and the van der Waals attraction between these particles
was considered as the driving force for forming agglomerations
[24,25]. As shown in Fig. 7, a dispersion boundary demarcates
the whole phase diagram into a well-dispersed region (D) and an
agglomerated phase region (A). Transparent nanocomposites are
expected only within the D region. The experimental dispersion
results of TiO2 NPs grafted with PGMA of different molecular
weights are also plotted within the phase diagram. The theoretical prediction and the experimental observations are in
agreement as at maximum graft densities the grafted particles
are within the well-dispersed region, and at very low graft
density they fall into the aggregated region. Moreover, for a fixed
grafted chain molecular weight the phase diagram precisely
captures the transition from well-dispersed state to aggregated
state. Similar to the dispersion diagram shown in Fig. 5, the
dispersion window defined by the region between maximum
achievable graft densities and critical graft densities to achieve
good dispersion is narrow.
Different from scaling law predictions about the graft density
relationship of “allophobic dewetting” [18,26,27], this parametric
model clearly demonstrates that the critical graft densities are
affected by both the grafted chain and the matrix molecular
weight. Fig. 4 further shows that with long grafted chains the
dispersion boundary becomes flatter, which is also consistent
with the tendency seen in Fig. 5. It is the utilization of a very small
molecular weight epoxy matrix (340 g mol1) that results in the
expansion of the D region and the near flat transition curve. It also
implies that due to the compromise between achievable graft
density and grafted chain molecular weight, grafting PGMA
chains with a small molecular weight at relatively high graft
densities would be ideal for obtaining good dispersions. During
the preparation of nanocomposites, the PGMA-grafted particles
were first mixed with the epoxy resin (part A). It was found that
the dispersion of particles in this step determines the final dispersion and appearance of the cross-linked nanocomposites. This
means the thermodynamic compatibility between grafted particles and epoxy matrix plays more important role in achieving
good dispersion of particles within the epoxy matrix. In the crosslink step, the epoxy chains will form connected network and their
molecular weight will increase dramatically. However, the PGMAgrafted particles were kinetically trapped and their dispersion
states were not changed. Meanwhile, it should be pointed out
that the synthesized near mono-disperse TiO2 particles and
grafted PGMA chains with very narrow PDI favor accurate prediction from the dispersion phase diagram. The final dispersion
and morphology of the grafted particles is determined by the
balance between the van der Waals attractions of the high-n TiO2
particles and entropic forces associated with the deformations of
the grafted PGMA chains [23,24]. The easy formation of anisotropic self-assembly instead of spherical agglomerates can be
understood from the fact that the agglomerated states are
actually very close to the dispersion boundary and the boundary
was obtained by equating the free energy between the individually dispersed state and the string-like morphology in this
modified model [24].
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P. Tao et al. / Polymer 54 (2013) 1639e1646
Fig. 6. Typical TEM images of (a, b) well-dispersed PGMA-10K brush (a graft density of 0.038 chain/nm2) grafted TiO2 NPs (10 wt%); typical (c, d) aggregated PGMA-10K chain (a
graft density of 0.016 chain/nm2) grafted TiO2 NPs (10 wt%) in an epoxy matrix at low and high magnifications.
3.4. Optical properties of TiO2/epoxy nanocomposites
Transparent TiO2/epoxy nanocomposites were prepared by using PGMA-brush-grafted particles as fillers. As shown in Fig. 8a, the
refractive index of the nanocomposite increased from 1.5 for neat
epoxy to 1.62 with 30 wt% anatase TiO2 NPs. The increase of
refractive index is accurately predicted by the rule of mixtures. The
transmittance spectra in Fig. 8b show that the thick sample
demonstrated a transparency of approximately 85% and 75% for
10 wt% and 30 wt% particle loading concentration, respectively.
However, the transparency decreased very rapidly in the 400e
600 nm range and the higher loading sample strongly blocked
the short wavelength blue light. It was noticed that the synthesized
TiO2 NPs appear light yellow in solvent despite their high transparency as shown in Fig. 1c. Hence, the resultant TiO2/epoxy
nanocomposites were also yellow as shown by the inset photographs, meaning that the nanocomposites absorb the low wavelength blue light. The absorption of blue light (400e600 nm)
becomes stronger for high filler loading and thicker nanocomposite samples.
Rayleigh scattering law as described in Eq. (2) was used to understand the decreased transparency in the long visible wavelength
range [4,28].
(
TPNC ¼ 0:9 exp
Fig. 7. Theoretical dispersion phase diagram prediction and comparison with experimental results for PGMA-grafted TiO2 NPs in an epoxy matrix. np is the number of
grafted PGMA chains per NP; r/Rg is the relative size of particles over the radius of
gyration of the grafted PGMA chains. Blue circles represent dispersed states and red
squares represent aggregated states observed experimentally (For interpretation of the
references to colour in this figure legend, the reader is referred to the web version of
this article.).
32p4 Fp xr3 n4m
l4
"
#)
2
np =nm 1
2
np =nm þ 2
(2)
where TPNC is the transmittance of polymer nanocomposites, l is
the wavelength of incident light, x is the optical path length, Fp is
the volume fraction of the particles, np and nm are the refractive
index of the particles and the matrix, respectively. Putting
np ¼ 2:5, nm ¼ 2:5 and optical path x ¼ 1 mm (nanocomposite
thickness of 1 mm) into Eq. (1), the optical transmittance spectra
after considering the Rayleigh scattering loss is also shown in
Fig. 8b. For the case of the 10 wt% TiO2/epoxy nanocomposite
sample, the theoretical prediction of transparency dependence on
wavelength agrees well with experimental observations in terms of
both the slope of the transmittance spectrum and the decreased
value. For the 30 wt% TiO2/epoxy nanocomposite sample, the
Rayleigh scattering model predicts an average decrease of transparency around 5%, which is lower than the experimentally
P. Tao et al. / Polymer 54 (2013) 1639e1646
1645
Fig. 8. Optical properties of neat epoxy and TiO2/epoxy nanocomposites: (a) Refractive index dispersion; (b) Experimentally measured and theoretically predicted transmittance
spectra of neat epoxy and TiO2/epoxy nanocomposites with a thickness of 1 mm. Assuming the maximum transmittance being 90%, the calculated spectra were obtained based on
the Rayleigh scattering law with different loading concentration and scattering center size (r, radius of scattering center). The insets compare the appearance of the prepared 10 wt%
and 30 wt% transparent nanocomposites filled with PGMA-10K brushigrafted TiO2 particles (with a graft density of 0.038 chain/nm2).
Fig. 9. Typical TEM images of epoxy nanocomposites filled with homogeneously dispersed 30 wt% PGMA-10K brush (with a graft density of 0.038 chain/nm2) grafted TiO2 particles
under low (a) and high (b) magnification.
observed transparency difference (10%) in the range of 600e
800 nm.
Considering the dense distribution of TiO2 NPs in the 30 wt%
nanocomposite sample (Fig. 9), it might be possible that the scattering centers are not single particles. However, Fig. 8b shows that
when imposing the assumption that the scattering center is composed of two NPs, the transparency loss is overestimated and the
slope is larger than the measured spectrum. Therefore, it appears
that due to good dispersion of the grafted particles within the
epoxy matrix, the transparency loss could be reasonably predicted
by the Rayleigh scattering law with scattering centers being individual particles. Actually, the theoretical predicted spectrum with
single particle as the scattering center shows a similar slope as
experimental measured curve. The two spectra are parallel with
each other within the range of 600e800 nm. The transparency
discrepancy might be attributed to the strict assumption regarding
the scattering particles in the Rayleigh model. The Rayleigh model
works better for dispersion of very low loading concentrations of
spherical particles [29,30]. The multiple scattering arising from
high filler loading and large thickness may be responsible for the
observed discrepancy in the 30 wt% TiO2/epoxy nanocomposites.
Furthermore, the high loading 30 wt% sample (n ¼ 1.62) would
have a 4% higher reflection loss at the air/composite interface
compared with the 10 wt% sample. This increased reflection loss
also contributes to the decreased transmittance and deviation from
theoretical prediction.
4. Conclusions
In summary, we report a simple approach to develop bulk
transparent, high-n TiO2/epoxy nanocomposites by filling a commercial epoxy resin with PGMA-brush-grafted anatase TiO2 NPs.
With the maximum achieved graft densities in the “grafting to”
method, the grafted PGMA chains existed in the brush regime. An
abrupt transition from good dispersion to agglomerate formation
arises when the graft density was too low to form polymer brushes.
Furthermore, we adapted a parametric model to quantitatively
analyze the dispersion transition and showed good agreement with
experimental observations. The prepared epoxy nanocomposites
filled with PGMA-brush-grafted TiO2 NPs demonstrated tunable
optical properties. Their refractive index increased linearly with the
filler volume fraction and their transparency was well described by
the Rayleigh scattering model.
Acknowledgment
This work was supported by the Engineering Research Center
Program (ERC) of the National Science Foundation under Cooperative Agreement EEC-0812056 and in part by New York State under
NYSTAR contract C090145. The authors also acknowledge financial
support by the Nanoscale Science and Engineering Initiative of the
National Science Foundation under NSF award number DMR0642573.
1646
P. Tao et al. / Polymer 54 (2013) 1639e1646
Appendix A. Supplementary data
Supplementary data related to this article can be found at http://
dx.doi.org/10.1016/j.polymer.2013.01.032.
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